U.S. patent number 7,219,015 [Application Number 10/787,791] was granted by the patent office on 2007-05-15 for methods for generating data set.
This patent grant is currently assigned to Swiss Reinsurance Company. Invention is credited to David N. Bresch, Pamela Heck, Gerry Lemcke.
United States Patent |
7,219,015 |
Bresch , et al. |
May 15, 2007 |
Methods for generating data set
Abstract
A computer method of generating a probabilistic dataset relating
to a weather event includes inputting data representative of an
historical weather event, and generating data representative of a
plurality of alternative events. The data for the alternative
events are generated, in certain embodiments, by a dependent
sampling process. In particular embodiments, the dependent sampling
process is a directed random walk process. Data for the alternative
events may include data relating to the geographical positions or
"tracks" of the event, data relating to atmospheric pressures, or
both.
Inventors: |
Bresch; David N. (Birmensdorf,
CH), Heck; Pamela (Zurich, CH), Lemcke;
Gerry (Rye, NY) |
Assignee: |
Swiss Reinsurance Company
(Zurich, CH)
|
Family
ID: |
34886856 |
Appl.
No.: |
10/787,791 |
Filed: |
February 26, 2004 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20050192751 A1 |
Sep 1, 2005 |
|
Current U.S.
Class: |
702/3;
73/170.16 |
Current CPC
Class: |
G01W
1/10 (20130101) |
Current International
Class: |
G01W
1/00 (20060101); G06F 19/00 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Barlow; John
Assistant Examiner: Kundu; Sujoy
Attorney, Agent or Firm: Barnes & Thornburg LLP
Claims
What is claimed is:
1. A computer method of generating a probabilistic data set
relating to a weather event, comprising the steps of: a) inputting
data representative of an historical track of a weather event, said
data including a plurality of points representative of geographical
positions along the historical track; and b) generating data
representative of a plurality of alternative tracks based on said
historical track, said data including a plurality of alternative
points representative of geographical positions along said
alternative tracks; c) wherein said alternative points are
generated from said points along the historical track by a
dependent sampling process; d) wherein the step of inputting data
representative of a track of an historical weather event includes
inputting data representative of intensity of the event; e) wherein
said data representative of intensity comprises atmospheric
pressure data associated with at least some of the plurality of
points along the historical track, said atmospheric pressure data
defining an historical pressure profile of the historical track;
and f) wherein the step of inputting data includes inputting data
representative of a plurality of historical tracks, and further
comprising the step of establishing a grid over a geographical area
of interest, said area including at least a portion of the
plurality of historical tracks.
2. The method of claim 1, wherein said dependent sampling process
is a directed random walk process.
3. The method of claim 1, wherein at least some of the plurality of
alternative tracks have starting points that differ from a starting
point of the historical track upon which said alternative tracks
are based.
4. The method of claim 1, wherein the step of generating data
representative of alternate tracks based on said historical track
comprises the steps of: 1) generating a series of random tuples
(x.sub.r,y.sub.r) for a historical point (x,y) of the historical
track; 2) calculating a sum of random deviations (x',y') of the
random tuples along the historical track; and 3) adding the sum of
random deviations (x',y') to the historical point (x,y) of the
historical track to produce alternative points along the
alternative tracks.
5. The method of claim 1, wherein the step of inputting data
representative of a track of an historical weather event comprises
inputting a longitude and a latitude to define each of a plurality
of points along said track.
6. The method of claim 1, wherein the step of inputting data
includes inputting data representative of a plurality of historic
tracks, and wherein the step of generating data includes generating
a plurality of alternative tracks for more than one of said
plurality of historical tracks.
7. The method of claim 1, wherein the step of inputting data
representative of an historical track includes the step of
inputting at least one of: 1) longitude and latitude of a plurality
of points representative of the historical track; 2) an azimuth
angle for at least some of the points along the historical track;
3) celerity for at least some of the points along the historical
track; 4) a rate of change of azimuth angle for at least some of
the points along the historical track; and 5) a rate of change of
celerity for at least some of the points along the historical
track.
8. The method of claim 1, further comprising the step of selecting
a subset of the data representative of the alternative tracks for
use in the probabilistic data set.
9. The method of claim 1, wherein the step of generating data
representative of alternative tracks includes the step of limiting
a variance of said alternative points from a respective historical
point in accordance with one or more physical laws.
10. The method of claim 1, wherein said atmospheric pressure data
includes an absolute pressure (P) and a derivative of absolute
pressure with respect to time (dP/dT).
11. The method of claim 1, wherein said atmospheric pressure data
includes a pressure distribution.
12. The method of claim 1, further comprising the step of
establishing a pressure climatology for selected cells in the grid,
based upon the atmospheric pressure data associated with at least
some of the plurality of points along the historical tracks located
within said selected grid cells.
13. The method of claim 12, wherein the pressure climatology for at
least one of the selected cells is a pressure distribution
function.
14. The method of claim 12, wherein the pressure climatology for a
selected cell in the grid is established from at least one of the
atmospheric pressure data associated with the selected cell and the
atmospheric pressure data associated with one or more cells
adjacent the selected cell.
15. The method of claim 14, wherein the pressure climatology for a
selected cell is established from a weighted averaging of pressure
data associated with the selected cell and pressure data associated
with one or more cells adjacent a selected cell.
16. The method of claim 14, wherein each cell in the grid is
assigned a land/sea value, and wherein pressure data associated
with an adjacent cell is used to establish the pressure climatology
of a selected cell only if the adjacent cell and the selected cell
have the same land/sea value.
17. The method of claim 12, comprising the additional step of
generating one or more alternative pressure profiles for one or
more of the historical tracks using the pressure climatology for
the selected cells in the grid.
18. The method of claim 12, comprising the additional step of
generating one or more pressure profiles for one or more of the
alternative tracks.
19. The method of claim 18, further comprising the additional step
of generating one or more alternative pressure profiles for one or
more of the alternative tracks using the pressure climatology for
the selected cells of the grid.
20. The method of claim 19, wherein at least one of the alternative
pressure profiles for the historical tracks, the pressure profiles
for the alternative tracks, and the alternative pressure profiles
for the alternative tracks are modified based, at least in part, on
the historical pressure profile along the historical track of the
associated weather event.
21. The method of claim 1, wherein the step of inputting data
includes inputting data representative of a plurality of historical
tracks and inputting data representative of atmospheric pressure
associated with at least some of the plurality of points along the
historical tracks, said atmospheric data defining historical
pressure profiles of the historical tracks, and wherein the step of
generating data includes generating a plurality of alternative
tracks for more than one of said plurality of historical tracks,
and further comprising at least one of the following steps: a)
generating one or more alternative pressure profiles for one or
more of the historical tracks; b) generating one or more pressure
profiles for one or more of the alternative tracks; and c)
generating one or more alternative pressure profiles for one or
more of the alternative tracks.
22. The method of claim 20, further comprising the step of
extracting a subset of data from the data representative of the
historical tracks, the alternative tracks, and the pressure
profiles, based on climatological conditions for a selected time
period.
23. A computer method for generating a probabilistic data set
relating to a weather event, comprising the steps of: (a) inputting
data representative of an historical weather event, said data
including a plurality of points representative of geographical
positions along a track of the historical weather event; and (b)
inputting data representative of atmospheric pressure associated
with at least some of the plurality of points along the historical
track, said atmospheric data defining a pressure profile of the
historical weather event; and (c) generating a plurality of
alternative pressure profiles associated with the track of the
historical weather event.
24. The method of claim 23, wherein the step of generating a
plurality of alternative pressure profiles comprises the steps of:
(d) identifying a point of occurrence of an absolute pressure
minimum along the track of the historical weather event; (e)
selecting an alternative pressure value at the point identified in
step (d); (f) adjusting pressure values at a plurality of other
points along the track of the historical weather event, in
accordance with the selected alternative pressure value, to create
an alternative pressure profile; and (g) repeating steps (d), (e),
and (f) to produce a plurality of alternative pressure profiles
associated with the track of the historical weather event.
25. The method of claim 23, further comprising the steps of
generating data representative of a plurality of alternative tracks
based on said track of the historical weather event, said data
including a plurality of alternative points representative of
geographical positions along said alternative tracks.
26. The method of claim 25, further comprising the step of
generating a plurality of alternative pressure profiles associated
with at least some of said plurality of alternative tracks.
27. The method of claim 26, wherein the step of generating said
plurality of alternative pressure profiles associated with said
plurality of alternative tracks comprises the steps of: (d)
identifying a point of occurrence of an absolute pressure minimum
along one of said alternative tracks; (e) selecting an alternative
pressure value at the point identified in step (d); (f) adjusting
pressure values at a plurality of other points along said
alternative track, in accordance with the selected alternative
pressure value, to create an alternative pressure profile; and (g)
repeating steps (d), (e), and (f) to produce a plurality of
alternative pressure profiles associated with said plurality of
alternative tracks.
28. The method of claim 26, wherein the step of generating a
plurality of alternative pressure profiles associated with at least
some of the plurality of alternative tracks comprises the steps of:
(d) identifying a pressure value at a first position along the
historical track, and setting a pressure value at a corresponding
position along an alternative track equal to the identified
pressure value; (e) determining a percentile of pressure change
along the historical track between said first location and a second
location; (f) varying the percentile by a selected amount; (g)
determining a pressure value at a second location of the
alternative track based upon the varied percentile; (h) repeating
steps (d), (e), (f), and (g) for additional points along the
alternative track to create an alternative pressure profile
associated with the alternative track; and (i) repeating steps (d),
(e), (f), (g), and (h) to create pressure profiles for other ones
of the plurality of alternative tracks.
29. The method of claim 28, wherein the percentile is varied by
approximately plus/minus fifteen percent.
30. The method of claim 28, comprising the step of creating
additional alternative pressure profiles by at least one of: (a)
selecting a different position along the historical track as a
starting point; and (b) varying the percentile by a different
amount.
Description
FIELD OF THE INVENTION
The present invention relates generally to methods of generating
data sets and, more particularly, computer methods for generating
data sets relating to weather events.
BACKGROUND AND SUMMARY
Each year, tropical cyclones (also referred to as hurricanes,
typhoons and tropical storms) cause severe damage in various parts
of the world. The occurrence of such weather events is difficult,
if not impossible, to predict over the long term. Even the path, or
track, of an existing storm can be difficult to predict over a
period of hours or days.
Nevertheless, insurance companies and other entities need to
develop ways of assessing the risks associated with such weather
events, and factoring that knowledge into the pricing of insurance
products and the magnitudes and frequencies of damages to expect
over time. Information is available for use in this regard in the
form of historical data on storms which have occurred through the
years. Approximately 80 such storms occur worldwide each year. Data
are collected on many of these storms, including positional data
for the storm path or "track," wind speeds, barometric pressures,
and other factors. Such storms are best documented in the North
Atlantic (i.e., the portion of the Atlantic Ocean north of the
equator), where reliable data for more than 100 years of activity
are available. Approximately 10 storms occur in the North Atlantic
region on an annual basis. Historical data are also available for
cyclones occurring in the Northwest Pacific, where approximately 26
storms occur each year. Suitable data for these Pacific storms are
available only for the last approximately 50 years. Less data are
available for storms in other regions.
Using all available historical data, information relating to a few
hundred storms are available for review by researchers and
scientists. Such information is useful in assessing risks
associated with storm damages in the subject areas. However, given
the unpredictable nature of storm behavior, and the number of
factors influencing such behaviors, the available data set of
historical storms is relatively small from a probabilistic
viewpoint. Given that this data set will grow by only a relatively
few storms per year, a problem exists with regard to performing
statistical analysis relating to the possibility of a storm
occurring at a particular location.
One manner in which this problem can be addressed is by generation
of simulated or "alternative" storms, and using data from such
"storms" to expand the data set available from historical records.
This approach can result in the availability of thousands, or even
tens or hundreds of thousands, of additional storms from which to
create data sets large enough to perform reliable statistical
analyses. The subject invention is directed to various embodiments
involving uses of computer methods for generating such expanded
probabilistic data sets.
One embodiment of the invention comprises a computer method for
generating a probabilistic data set relating to a weather event,
such as a tropical cyclone, or hurricane, typhoon, or tropical
storm. This embodiment of the method includes the steps of
inputting data representative of an historical track of a weather
event and generating data representative of a plurality of
alternative tracks based on the historical track. The data points
representative of the alternative tracks are generated from
respective points along the historical track by a dependent
sampling process. In certain embodiments, the dependent sampling
process is a directed random walk process.
In one embodiment, the step of generating data representative of
alternative tracks based on the historical track comprises the
steps of generating a series of random tuples (x.sub.r,y.sub.r) for
a historical point (x,y) of the historical track, calculating a sum
of random deviations (x',y') of the random tuples along the
historical track, and adding the sum of random deviations (x',y')
to the historical point (x,y) of the historical track to produce
alternative points along the alternative tracks.
The data representative of the historical track(s) include a
plurality of points representative of geographical positions along
the historical track(s). The generated data representative of a
plurality of alternative tracks includes a plurality of alternative
points representative of geographical positions along the
alternative tracks. In one embodiment, at least some of the
plurality of alternative tracks associated with a particular
historical track have starting points that differ from a starting
point of the historical track upon which the alternative tracks are
based. The data representative of the historical track may comprise
longitude and latitude data to define a location of each of a
plurality of points.
In certain embodiments of the method, the step of inputting data
representative of an historical track includes the step of
inputting at least one of: longitude and latitude of a plurality of
points representative of the historical track; an azimuth angle for
at least some of the points along the historical track; celerity
for at least some of the points along the historical track; a rate
of change of azimuth angle for at least some of the points along
the historical track; and a rate of change of celerity for at least
some of the points along the historical track. Alternatively, the
latter values (azimuth, celerity, and rates of change of azimuth
and celerity) may be calculated from longitude and latitude data
recorded at periodic time intervals.
Some embodiments of the subject method further comprise the step of
selecting a subset of the data representative of the alternative
tracks for use in the probabilistic data set. In these or other
embodiments, the step of generating data representative of
alternative tracks includes the step of limiting a variance of the
alternative points from a respective historical point in accordance
with one or more physical laws.
In certain embodiments of the subject method, the step of inputting
data representative of a track of an historical weather event
includes inputting data representative of an intensity of the
event. The data representative of intensity may comprise
atmospheric pressure data associated with at least some of the
plurality of points along the historical track. The atmospheric
pressure data defines an historical pressure profile of the
historical track. The atmospheric pressure data may include an
absolute pressure and a derivative of (or change in) absolute
pressure with respect to time. In certain embodiments, the
atmospheric pressure data includes one or more pressure
distributions. In some embodiments of the subject method, the step
of inputting data includes inputting data representative of a
plurality of historical tracks, and the step of establishing a grid
over a geographical area of interest including at least a portion
of the plurality of tracks. These embodiments may further comprise
the step of establishing a pressure climatology for selected cells
in the grid, based upon the atmospheric pressure data associated
with at least some of the plurality of points along the historical
tracks located within the selected grid cells. The pressure
climatology for the selected cells may be a pressure distribution
function. The pressure climatology for a selected cell in the grid
may be established from the atmospheric data associated with the
selected cell and/or the atmospheric pressure data associated with
one or more cells adjacent the selected cell (i.e., one or more
neighboring cell). In certain embodiments, the pressure climatology
for a selected cell is established from a weighted averaging of
pressure data associated with the selected cell and pressure data
associated with one or more neighboring cell.
In certain embodiments, each cell in the grid is assigned a
land/sea value. In these embodiments, pressure data associated with
an adjacent cell is used to establish the pressure climatology of
the selected cell only if the adjacent and the selected cell have
the same land/sea value.
Certain embodiments of the subject method comprise the additional
step of generating one or more alternative pressure profiles for
one or more of the historical tracks using the pressure climatology
for the selected cells in the grid. In addition, one or more
pressure profiles may be generated for one or more of the
alternative tracks. One or more alternative pressure profiles may
also be generated for one or more of the alternative tracks using
the pressure climatology for the selected cells of the grid. In
some embodiments, at least one of the alternative pressure profiles
for the historical tracks, the pressure profiles for the
alternative tracks, and the alternative pressure profiles for the
alternative tracks are modified based, at least in part, on the
historical pressure profile along the historical track of the
associated weather event.
In certain embodiments of the invention, the step of inputting data
includes inputting data representative of a plurality of historical
tracks and inputting data representative of atmospheric pressure
associated with at least some of the plurality of points along the
historical tracks. The atmospheric data defines historical pressure
profiles of the historical tracks. In these embodiments, the step
of generating data includes generating a plurality of alternative
tracks for more than one of the historical tracks. Further, these
embodiments include at least one of the following steps: a)
generating one or more alternative pressure profiles for one or
more of the historical tracks; b) generating one or more pressure
profiles for one or more of the alternative tracks; and c)
generating one or more alternative pressure profiles for one or
more of the alternative tracks. These or other embodiments of the
subject method may further comprise the step of extracting a subset
of data from the data representative of the historical tracks, the
alternative tracks, and the pressure profiles, based on
climatological conditions for a selected time period.
Additional features and advantages will become apparent to those
skilled in the art upon consideration of the following detailed
description of illustrative embodiments exemplifying the best mode
of carrying out the method as presently perceived.
BRIEF DESCRIPTION OF DRAWINGS
The patent or application file contains at least one drawing
executed in color. Copies of this patent application publication
with color drawing(s) will be provided by the Office upon request
and payment of the necessary fee.
The present disclosure will be described hereafter with reference
to the attached drawings which are given as non-limiting examples
only, in which:
FIG. 1 is a flow chart which illustrates the overall operation of
one embodiment of the method of the present invention.
FIG. 2 is a flow chart which further illustrates the step of
inputting data for historical storms in the embodiment of FIG.
1.
FIG. 3 is a flow chart which further illustrates the step of
establishing a climatology in the embodiment of FIG. 1.
FIG. 4 is a flow chart which further illustrates the step of
producing alternative storm tracks in the embodiment of FIG. 1.
FIG. 5 is a flow chart which further illustrates the step of
producing alternative pressure evolutions in the embodiment of FIG.
1.
FIG. 6 is a flow chart which further illustrates the steps of
selecting a subset of alternative storms and calculating the wind
field in the embodiment of FIG. 1.
FIG. 7 illustrates a method of generating points of a probablistic
data set which are representative of a portion of an alternative
storm track.
FIG. 8a illustrates a plurality of alternative storm tracks
generated by the method of FIG. 7 using a normally-distributed
random walk.
FIG. 8b illustrates a plurality of alternative storm tracks
generated by the method of FIG. 7 using an evenly-distributed
random walk.
FIG. 8c illustrates a plurality of alternative storm tracks
generated by the method of FIG. 7 using a directed random walk.
FIG. 9a illustrates a plurality of alternative storm tracks, each
originating at the starting point of a respective historical
track.
FIG. 9b illustrates a plurality of alternative storm tracks, each
originating at an alternative starting point relative to a
respective historical track.
FIG. 10 illustrates a plurality of historical and alternative storm
tracks superimposed over a portion of a map.
FIG. 11 illustrates a plurality of alternative pressure evolutions
for each of a plurality of storms.
DETAILED DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flow chart which illustrates the overall operation of
one embodiment of the subject method. The first step in this
embodiment is inputting data for a plurality of historical storms.
This step is represented by block 12 of FIG. 1. Such data includes
geographical information defining the tracks of the respective
historical storms and intensity data to indicate the strength of
the storm. One source of such data is the National Hurricane Center
("NHC") which is part of the National Oceanic and Atmospheric
Administration ("NOAA"). Geographic and intensity data for
hurricanes and tropical cyclones and storms may be viewed at, and
is available from, the NHC website at www.nhc.noaa.gov. Following
the inputting of this data, a climatology is established in the
area of interest. This operation is represented by block 14 in FIG.
1. After establishment of the climatology, alternative storm tracks
are produced for each of the historical tracks in the inputted
data. This step is represented by block 16.
Following production of the alternative storm tracks, a plurality
of alternative pressure evolutions are produced for the historical
and alternative tracks. This step is represented in FIG. 1 by block
18. Production of the alternative storm tracks, and the alternative
pressure evolutions for the historical and alternative tracks,
creates a relatively large universe of storms (both historical and
alternative). A subset of the alternative storms is selected based
on climatological data. This step is represented by block 20.
Finally, wind fields are calculated for specific points of
interest. This step is represented in the flow chart of FIG. 1 by
block 22. Each of steps 12 22 are discussed in additional detail
below in connection with the flow charts of FIGS. 2 6.
FIG. 2 is a flow chart which further illustrates the step of
inputting data for historical storms in the embodiment of FIG. 1.
The first operation in this step is represented by block 24 labeled
"Read Raw Data." As previously indicated, one source of data on
historical storms is the National Hurricane Center. These data
include geographical (i.e., latitude and longitude) data which
define individual nodes of the historical track. The locations of
storms are generally reported at six hour time intervals. In many
instances, intensity data is also provided in the form of a
pressure measurement taken in the vicinity of the center of the
node. In the event a central pressure measurement is not provided,
a pressure may be calculated from the maximum sustained wind also
available on the site. These operations are represented by decision
block 26 and processing block 28.
After reading the raw data and, if necessary, calculating
pressures, additional calculations are performed to determine
celerity, azimuth angles and Saffir-Simpson classes. These
calculations are represented in the flow chart of FIG. 2 by block
30. At this point, the data are checked and verified (block 32).
After those operations, the original data may be interpolated to
enhance resolution. That is, additional geographical points or
nodes may be defined between the "six hour nodes" available in the
raw data. The six hour nodes are interpolated to allow for a better
geographical resolution. In one embodiment, the data are
interpolated to 0.2 degree steps. Such interpolation allows for the
generation of smoother, alternative storm tracks, and enhances the
overall operation of the subject method. This operation is
represented by block 34 of FIG. 2.
The last operation in the step of inputting historical data relates
to the addition of "on-land" flags. When a storm moves from a
position over water to a position over land (or vice versa),
substantial pressure changes are observed. Accordingly, landfall
and land leave points are determined and entered into the data for
use in subsequent steps of the process. This operation is
represented in the embodiment of FIG. 2 by block 36.
FIG. 3 is a flow chart which further illustrates the step of
establishing a climatology in the embodiment of FIG. 1. Even though
records of more than 100 years of reliable pressure data exist,
this historical data is preferably preprocessed in order to obtain
a more consistent database by the methods described herein. The
first operation in the step of establishing a pressure climatology
is establishment of a 1.degree. by 1.degree. grid over the
geographical area of interest. This operation is represented by
step 38 in the embodiment of FIG. 3. The original data includes
both the absolute pressure at specified locations, and the change
in pressure (i.e., the pressure derivative). These data are matched
with the individual grid locations (block 40). Some locations in
the grid will have many observed pressure and pressure derivative
values. Other locations have fewer observed values, and yet others
may have none.
Following this operation, minimum pressures based on the sea
surface temperature (SST) climatology are added. That is, for each
location in the grid, the lowest pressure associated with the
highest SST ever observed in that particular location is entered.
This value acts as a "floor" for alternative pressure values
associated with each location in the grid that may be selected (as
discussed in additional detail below) in connection with
alternative pressure evolutions for the historical and/or
alternative storm tracks. This operation is represented by block 42
in the embodiment of FIG. 3.
After addition of minimum pressures, the pressure climatology is
smoothed. The goals of the smoothing process include one or more of
the following: to obtain full coverage of the area of interest; to
smooth variations in the distributions of pressures and pressure
derivatives from one grid to its neighboring grids; to smooth
variations in distributions of minimums, maximums and means of the
absolute pressures and pressure derivatives; and to obtain the same
number of "observations" at each grid location. This smoothing
process leads to a more consistent set of pressure related values
for the area of interest to be used in a sampling process to be
described further below. In the particular embodiment being
described, the quantities to be smoothed are not scaler quantities
(such as, a mean pressure quantity at each location), but rather
are pressure-related distributions for each location. Accordingly,
the smoothing process is relatively more complex.
In order to achieve the goals stated above, one embodiment of the
subject method follows the approach set forth below. Other
approaches may be used, and some may very well be comparable to, or
even preferred over, this approach. The approach is as follows:
The number of valid observations at each location is determined. In
this embodiment, up to 260 observations for each location may be
entered. Some locations may have this many observations (or more)
while other locations may have fewer or none. All non-valid data
are replaced. The distinction between valid observations and
non-valid observations is based upon the fact that pressure values
below 800 hPa are impossible, and thus not valid. After all valid
observations are entered for each location, the subject method
loops through the data location, applying the following procedure
at each location (referred to as the "center location"): 1) Obtain
all valid observations for the center location and all neighboring
locations (i.e., all grid cells surrounding the "center" cell)
having the same land/sea value. That is, if the center location is
a sea location, only neighboring locations that are also sea
locations are considered. If the center location is a land
location, only neighboring locations that are also land locations
are considered. Thus, land and sea observations are not mixed in
the smoothing process. 2) Construct the pressure distribution file
for all points. The center location observations are more heavily
weighted, for example, by counting them twice. Depending on the
number of neighboring locations having the same land/sea values and
the number of valid observations at each location, an arbitrary
number of observations for this particular pressure distribution
file is obtained. 3) Use a cubic spline to interpolate the pressure
distribution function to a standard number of observations (for
example, 1000 observations for each location).
The above approach will produce a data set having a standard number
(for example, 100) of pressure and pressure derivative observations
at each grid cell which is not separated by more than 1 degree from
an original cell. By iteration, one can in theory fill all gaps
existing in the area of interest.
The above-described approach accomplishes the goals set forth
previously. Locations in which historical observations are not
available within the area of interest are "filled in," and
variations across the area of interest are smoothed. However, sharp
pressure gradients which occur at land/sea transition locations are
maintained.
The pressure climatology smoothing operation is represented in FIG.
3 by block 44. It should be noted that, in the described
embodiment, both a land climatology and a sea climatology are
established and smoothed in the manner described above.
FIG. 4 is a flow chart which further illustrates the step of
producing alternative storm tracks in the embodiment of FIG. 1. The
first step in this operation is selection of one of the plurality
of historical tracks (i.e., longitude and latitude data) inputted
in the first step of the overall process illustrated in FIG. 1. The
selection operation is represented in the flow chart of FIG. 4 by
block 46. An alternative track is then generated for the selected
historical track. The specific manner in which each alternative
track is generated is described in additional detail below. This
operation is represented in the flow chart of FIG. 4 by block 48. A
plurality (N) of alternative tracks are produced. In the embodiment
of FIG. 4 this is illustrated by the presence of decision block 50
and the resulting loop. Similarly, a plurality of tracks are
generated for each historical track. This aspect of the operation
is illustrated by the presence of decision block 52 and the
resulting loop.
Following generation of the alternative tracks, the embodiment of
the method illustrated in FIG. 1 produces an alternative pressure
evolution ("APE") for each of the historical tracks and the
alternative tracks. FIG. 5 is a flow chart which further
illustrates the step of producing APEs in the embodiment of FIG. 1.
The first operation in this step is selection of an historical
track. This operation is represented in FIG. 5 by block 54. The
next operation in this step is generation of an APE for a selected
historical track. This operation is represented in FIG. 5 by block
56. A plurality (M) of APEs are generated. This feature is
represented schematically by decision block 58, and the resulting
loop.
In addition to generating an APE for each historical track, it is
desirable to generate an APE for each alternative track associated
with each historical track. Accordingly, after generation of an APE
for the first historical track, the method of this embodiment
associates each alternative track generated from the selected
historical track with the original pressure evolution of the
historical track. This operation is represented in FIG. 5 by block
60. An APE is then generated for the alternative track (block 62).
The methodology for generating the APE is the same as was used in
connection with the operation referred to in connection with block
56. A specific sampling process applicable to this operation is
discussed in additional detail below. A plurality (M) of APEs are
generated for each alternative track. This feature is illustrated
in FIG. 5 by decision block 64, and the resulting loop. APEs are
then similarly generated for each of the plurality (N) of
alternative tracks associated with each historical track. This
feature is illustrated by decision block 66 in FIG. 5, and the
resulting loop. Finally, the operation continues in this manner
until APEs have been generated for all historical tracks and all
associated alternative tracks. This feature is illustrated in the
embodiment of FIG. 5 by decision block 68, and the resulting
loop.
FIG. 6 is a flow chart which further illustrates the steps of
selecting a subset of alternative storms based on climatology in
the embodiment of FIG. 1. The first operation in this step is
selection of alternative tracks to create a plurality of "clone"
years. Specifically, each historical year includes a plurality of
historical storms. In accordance with the above discussion, a
plurality (N) of alternative tracks are created for each historical
track in a given year. However, since the alternative tracks are
produced by a random process (albeit one that uses a dependent
sampling technique), some of the alternative tracks for a given
year are more likely to occur than others. The selection process is
based upon knowledge of the climatology for the actual year in
which the associated historical storm tracks occurred. In other
words, alternative tracks which might be judged as relatively
unlikely to occur in actuality are deselected, based on established
climatological knowledge. Thus, from the universe of alternative
tracks available to create a "clone" year, a selection is made to
include certain of the alternative tracks and exclude others. This
operation is illustrated by block 70 in FIG. 6.
An "adjustment" made to the data for the selected storms relates to
the previously discussed "on-land" flags. Since pressures increase
rapidly when a storm moves from over water to over land, pressure
data associated with the alternative tracks are adjusted to reflect
this phenomena. This operation is represented by block 72 in the
flow chart of FIG. 6.
The final step in the overall methodology illustrated by the flow
chart of FIG. 1 relates to calculation of the wind field for
particular points along each storm path. Such calculations include
application of Holland's Formula, accounting for extra-tropical
transitions, and accounting for directional roughness values. These
operations are represented by blocks 74, 76, 78, and 80 in the flow
chart of FIG. 6.
As previously noted, the alternative storm tracks are generated by
a dependent sampling technique. FIG. 7 illustrates a method of
generating points of a probabilistic data set which are
representative of an alternative storm track. With reference to
FIG. 7, line segment 100 represents a portion of an historical
storm track. For purposes of discussion, an x-y coordinate system
has been superimposed such that line 100 may be represented by
three points, as follows:
##EQU00001## ##EQU00001.2##
Corresponding points of an alternative track, represented by line
102, are produced by generating a series of random tuples
(x.sub.r,y.sub.r) for each point of the historical track, then
calculating the cumulative sum (x',y') of these random numbers
along the track (i.e., summing up random deviations along the
track), and then adding these accumulated random deviations (x',
y') to the historical track (x,y). The resulting points define the
alternative track. In the example of FIG. 7, the random tuples
are:
##EQU00002## ##EQU00002.2## The cumulative sums along the
alternative track are:
'' ##EQU00003## Finally, the points on the generated track (line
102) are obtained as follows:
'' ##EQU00004##
There are different ways to generate the random numbers, either by
independently sampling from a normal or uniform distribution, or by
a dependent sampling technique (such as, a directed random walk).
Using the latter, a subsequent point can only deviate to a certain
degree from a previous point. As will be illustrated in additional
detail below, a dependent sampling technique (particularly, a
directed random walk) generates more realistic alternative storm
tracks.
FIGS. 8a 8c illustrate alternative storm tracks generated by the
above-described technique, using both independent and dependent
sampling. FIG. 8a illustrates the results achieved when the random
numbers are generated by independent sampling from a normal
distribution. In FIG. 8a, heavy line 104 represents the historical
track. The remaining lines represent alternative tracks. The
alternative tracks illustrate erratic storm movements which are not
likely to occur in nature.
FIG. 8b shows historical track 104 and a plurality of alternative
tracks generated by an independent sampling technique wherein the
random numbers are generated from a uniform distribution. The
alternative tracks in this example are much smoother than those
illustrated in FIG. 8a. However, the alternative tracks in FIG. 8b
continue to exhibit unrealistic "movements" at numerous points
along the track.
FIG. 8c shows historical track 104 and a plurality of alternative
tracks generated by a dependent sampling technique. In FIG. 8c,
each point along an alternative track can only deviate to a certain
degree from the previous point. As the results illustrate, this
"directed random walk" generates alternative tracks which are more
realistic than those illustrated in FIGS. 8a and 8b.
FIG. 9a illustrates the results produced when a plurality of
alternative tracks are generated from each of a relatively larger
number of historical tracks. In the illustration of FIG. 9a, each
historical track, and its respective associated alternative tracks,
begins at a common point (see, for example, the tracks beginning in
the lower right portion of FIG. 9a). FIG. 9b illustrates a similar
number of tracks, but incorporates a refinement that is an aspect
of the present invention. The refinement involves selecting
alternative starting points for each of the plurality of
alternative tracks associated with a particular historical track.
The effects of this change are readily apparent by the differences
in the lower right portions of FIG. 9a and FIG. 9b, respectively.
This change alleviates somewhat an unnatural "clustering" of
alternative and historical tracks which is apparent in the
illustration of FIG. 9a.
FIG. 10 illustrates the result which is obtained when a relatively
large number of historical tracks, and a plurality of alternative
tracks associated with each historical track, are superimposed upon
a map of the Caribbean and North Atlantic.
The sampling process by which the alternative pressure evolutions
(APEs) are produced will now be described. As discussed above in
connection with FIG. 3, a pressure climatology is established and
smoothed. Subsequent to these steps, an historical storm is
selected for sampling. At each location, the historical pressure is
first noted. Then, an alternative pressure value is selected from
the pressure distributions available for that location from the
smoothed pressure climatology. The chosen pressure is then
associated with that geographical point of the historical track to
produce an alternative pressure evolution for that point. This
process is repeated to create a plurality (M) of alternative
pressure values for each point, and thus a plurality of alternative
pressure evolutions for the historical track.
One manner of producing an alternative pressure evolution for a
selected track may be referred to as the "minimum" method. In this
method, the location (latitude and longitude) of the absolute
pressure minimum in the selected track is identified. A new
pressure value is then selected according to a pressure
distribution function at that location. The selection may be based
on a random choice. Once the new minimum value is chosen, all other
pressure values along the selected track are adjusted accordingly,
leaving only the first and last values unchanged. This results in
an alternative pressure evolution which mirrors the shape of the
selected track, but in which the absolute values of the pressures
will vary at each location (except for the very first and very last
locations along the track). Landfall and landleave locations may
also be identified to assure that appropriate values are set in the
alternative pressure evolutions at these locations.
Another method by which alternative pressure evolutions may be
generated can be described as the "percentile" method. This method
is based on pressure differences over time (dp/dt), along with
information from the historical track. The steps for computing a
pressure evolution for an alternative track are as follows: a) At
time t=0 along the alternative track, the pressure value p(0) is
set equal to the pressure value of the historical storm at time
t=0. b) At time t=1, the pressure value along the alternative track
is determined by first determining the percentile of the pressure
change along the historical track between times t=0 and t=1. This
value is located on the pressure distribution curve for the
historical track at location x=1. The percentile is varied by a
certain amount, and a pressure change value corresponding to the
varied percentile is located in the pressure distribution for
location x=1 of the alternative track. The pressure value at time
t=1 in the alternative track is then equal to the pressure at time
t=0 plus the value located in the alternative track pressure
distribution. c) The above steps are repeated for time t=2, with
reference back to the values determined at time t=1.
The percentile is preferably varied according to a uniform
distribution. Variance is preferably approximately plus/minus 15%.
A second alternative pressure evolution may be created by starting
from the last time step and following the same procedure working in
reverse to time t=0. A third alternative pressure evolution may be
determined by taking a weighted average of the first and second
pressure evolutions, giving more weight to the first near the
beginning of the track and more weight to the second near the
track's end. It will be appreciated by those of skill in the art
that other variations may be similarly determined to produce
additional pressure evolutions.
The process of generating alternative pressure evolutions is
repeated for each of the historical tracks inputted in the initial
step, and for each of the alternative tracks generated from each of
the historical tracks. Thus, if there are N alternative tracks
generated for each historical track, and if there are M APEs
generated for each of the historical and alternative tracks, a
total of (N+1).times.M "artificial" storms are generated for each
historical storm for which data are available. That is, each track
(whether it is a historical or an alternative one) is associated
with M hypothetical pressure evolutions.
FIG. 11 illustrates APEs generated for a plurality of storm tracks.
In each of the illustrations of FIG. 11, the pressure evolution of
a selected storm track is illustrated by a dark line, while APEs
generated for the selected storm track are represented by lighter
lines. As previously discussed, the profiles or shapes of the APEs
are similar to the selected track. However, the absolute pressure
values at any given location along the track differ, as
illustrated.
The choice of alternative pressures for each point of the
historical pressure evolution is subject to some constraints. For
example, the alternative pressure value chosen for a particular
point will not exceed pressure values that have never been observed
at that particular point, or those that have been determined using
the extension of the climatology based on the SST. Furthermore, if
in the historical pressure evolution, an unusual pressure variation
occurs at a particular location, then similarly unusual variations
may be selected for the APEs at that location. Pressure variations
which are not possible in nature, or would be extremely unlikely to
occur at a given location, are also avoided. The pressure
distributions developed in connection with the establishment of the
pressure climatology discussed in connection with FIG. 3 are used
to facilitate satisfaction of these constraints.
Although the present disclosure has been described with reference
to particular means, materials and embodiments, from the foregoing
description, one skilled in the art can easily ascertain the
essential characteristics of the present disclosure and various
changes and modifications may be made to adapt the various uses and
characteristics without departing from the spirit and scope of the
present invention as set forth in the following claims.
* * * * *
References